Finite Group Databasebeta

← C2×#10595129 #11900444

Subgroups — C2×#10595129 #11900444

Order 1152.

3973 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C23×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#64148C211yesmaximal, characteristic, complemented
4C2×C3×#937C211yesmaximal, characteristic, complemented
5C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
6C2×#63982C211yesmaximal, characteristic, complemented
7C2×#63977C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63971C211yesmaximal, characteristic, complemented
10C2×#63969C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595129C2116yesmaximal, direct product factor
13C2×#63899C211yesmaximal, characteristic, complemented
14C2×#63890C211yesmaximal, characteristic, complemented
15C2×#63880C211yesmaximal, characteristic, complemented
16C2×#63877C211yesmaximal, characteristic, complemented
17C2×#5586—31nomaximal
18C2×#5547—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C23×C3⋊Dic3C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic, complemented
28C22×#627C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#624C2211yescharacteristic, complemented
32C2×#3804—28no—
33C2×#3804C2218yescomplemented
34C22×D3×Dic3—28no—
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic
39C22×D3×Dic3C2218yescomplemented
40C2×#3757C2211yescharacteristic, complemented
41#64148C2218yescomplemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3750C2211yescharacteristic, complemented
44C2×C3×#217C2211yescharacteristic
45C2×C3×#217C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#937C2218yescomplemented
48C3×D4×Dic3C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C2×C3×C4×Dic3C2211yescharacteristic, complemented
53#63982C2218yescomplemented
54#63977C2218yescomplemented
55Dic3×#67C2218yescomplemented
56#63971C2218yescomplemented
57#63969C2218yescomplemented
58C2×#3724C2211yescharacteristic, complemented
59C2×#3724C2211yescharacteristic, complemented
60C2×Dic3⋊Dic3C2211yescharacteristic, complemented
61C2×Dic3⋊Dic3C2211yescharacteristic, complemented
62C2×#3722C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64C2×(C2×D3)⋊Dic3C2211yescharacteristic
65C2×Dic32C2211yescharacteristic, complemented
66#63952C2218yescomplemented
67#63899C2218yescomplemented
68#63890C2218yescomplemented
69#63880C2218yescomplemented
70#63877C2218yescomplemented
71C24×Dic3—31no—
72C22×#237—31no—
73C22×#235—31no—
74C23×C4×D3—31no—
75C2×C3×#120—31no—
76C2×C3×C4×D4—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939—61no—
82C2×#937D311yescharacteristic, complemented
83C2×#935—31no—
84C2×D4×Dic3—31no—
85C2×D4×Dic3D311yescharacteristic, complemented
86C2×C4×#67—31no—
87C2×C4×#67—31no—
88#5586—316no—
89#5547—316no—
90C2×#896—31no—
91C2×#894—31no—
92C2×#886—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#877—31no—
102C2×C4×D12—31no—
103C2×#872—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—24no—
110C23×C3×D3C2314yes—
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C2×C32×D4—24no—
114C2×C32×D4C2314yes—
115C22×C32×C4C2311yescharacteristic
116C2×#638—24no—
117C2×#638—24no—
118C2×#638C2314yes—
119C2×#638C2314yescomplemented
120C22×C3⋊Dic3—24no—
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2314yes—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C2×C3×#67—24no—
126C2×C3×#67—24no—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C22×C3×Dic3—24no—
130C22×C3×Dic3—24no—
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yes—
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2314yescomplemented
139C2×#627—24no—
140C2×#627C2314yescomplemented
141C2×#626—24no—
142C2×#626—24no—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#624—24no—
146C2×#624C2314yescomplemented
147#3804—232no—
148C2×D3×Dic3—24no—
149C2×D3×Dic3—24no—
150C2×D3×Dic3—24no—
151C2×D3×Dic3—232no—
152C2×D3×Dic3D418yescomplemented
153C2×D3×Dic3C2314yes—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yes—
157#3757C2314yescomplemented
158#3752C2314yescomplemented
159#3750C2314yescomplemented
160C3×#217C2314yes—
161C3×#217C2314yes—
162C3×#217C2314yescomplemented
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×C4⋊Dic3C2314yescomplemented
166C3×C4×Dic3C2314yescomplemented
167#3724C2314yescomplemented
168#3724C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171#3722C2314yescomplemented
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174Dic32C2314yescomplemented
175C2×#525—91noSylow
176C25×C3—31no—
177C24×D3C2×D311yescharacteristic
178C22×C3×D4—21no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4C2×D311yescharacteristic
182C22×C3×D4C2×D311yescharacteristic
183C23×C3×C4—31no—
184C23×C3×C4—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—61no—
192C22×#67—61no—
193C22×#67C2×D311yescharacteristic
194C22×#67C2×D311yescharacteristic
195C23×Dic3—31no—
196C23×Dic3—31no—
197C23×Dic3—31no—
198C23×Dic3—31no—
199C23×Dic3—31no—
200C23×Dic3—31no—
201C23×Dic3—38no—
202C23×Dic3—61no—
203C23×Dic3—68no—
204C23×Dic3C2×D311yescharacteristic
205C23×Dic3C2×D311yescharacteristic, complemented
206C2×#237—38no—
207C2×#237—68no—
208C2×#235—38no—
209C2×#235—68no—
210C22×D12—31no—
211C22×D12—31no—
212C22×C4×D3—31no—
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—38no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—68no—
220C22×Dic6—31no—
221C22×Dic6—31no—
222C3×#120—38no—
223C3×C4×D4—38no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C42—31no—
231#953—38no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—61no—
237C2×#217C2×D311yescharacteristic
238C2×#217C2×D311yescharacteristic
239C2×#217C2×D311yescharacteristic, complemented
240#939—38no—
241#939—38no—
242#939—38no—
243#939—68no—
244#937C2×D318yescomplemented
245#935—38no—
246D4×Dic3—38no—
247D4×Dic3C2×D318yescomplemented
248C4×#67—38no—
249C4×#67—38no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—61no—
257C2×(C2×D3)⋊C4C2×D311yescharacteristic
258C2×(C2×D3)⋊C4C2×D311yescharacteristic
259C2×C4⋊Dic3—31no—
260C2×C4⋊Dic3—31no—
261C2×C4⋊Dic3C2×D311yescharacteristic, complemented
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—61no—
271C2×C4×Dic3—31no—
272C2×C4×Dic3—31no—
273C2×C4×Dic3C2×D311yescharacteristic, complemented
274#896—38no—
275#894—38no—
276#886—38no—
277#884—38no—
278#883—38no—
279#882—38no—
280#67⋊C4—38no—
281#67⋊C4—38no—
282#878—38no—
283#878—38no—
284#878—38no—
285#877—38no—
286C4×D12—38no—
287#872—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2412yes—
296C23×C32C2411yescharacteristic
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3C2412yes—
301C22×C3×D3—232no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—28no—
307C22×C3×D3—28no—
308C22×C3×D3—28no—
309C22×C3×D3C2×D414yes—
310C22×C3×D3#4114yescomplemented
311C22×C3×D3C2412yes—
312C22×C3×D3C2412yes—
313C32×D4—28no—
314C2×C32×C4—22no—
315C2×C32×C4C2412yes—
316#638—28no—
317#638—28no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—28no—
321C2×C3⋊Dic3C2×D414yes—
322C2×C3⋊Dic3C2412yes—
323C2×C3⋊Dic3C2412yes—
324C2×C3⋊Dic3C2412yes—
325C3×#67—28no—
326C3×#67—28no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—28no—
333C2×C3×Dic3—28no—
334C2×C3×Dic3C2×D414yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2412yes—
340C2×C3×Dic3C2412yes—
341#627—28no—
342#626—28no—
343#626—28no—
344#624—28no—
345D3×Dic3—28no—
346D3×Dic3—28no—
347D3×Dic3—28no—
348D3×Dic3C2×D4116yescomplemented
349C22×#41—91no—
350C24×C4—91no—
351#525—916no—
352C2×#123—91no—
353C2×#123—91no—
354C2×C22⋊Q8—91no—
355C2×C22⋊Q8—91no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#120—31no—
359C2×#120—91no—
360C2×C4×D4—31no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C2×C4×D4—91no—
364C2×#117—91no—
365C24×C3—21no—
366C24×C3—21no—
367C24×C3—31no—
368C24×C3—31no—
369C24×C3—34no—
370C24×C3—64no—
371C24×C3—64no—
372C24×C3—64no—
373C24×C3C22×D311yescharacteristic
374C24×C3C22×D311yescharacteristic
375C24×C3C22×D311yescharacteristic
376C24×C3C22×D311yescharacteristic
377C23×D3—24no—
378C23×D3—24no—
379C23×D3—24no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—61no—
383C23×D3C22×D314yes—
384C23×D3C22×D311yescharacteristic
385C23×D3C22×D311yescharacteristic
386C2×C3×D4—24no—
387C2×C3×D4—24no—
388C2×C3×D4—24no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—44no—
392C2×C3×D4—64no—
393C2×C3×D4—64no—
394C2×C3×D4C22×D314yes—
395C2×C3×D4C22×D314yes—
396C22×C3×C4—21no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—34no—
404C22×C3×C4—34no—
405C22×C3×C4—64no—
406C22×C3×C4—64no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C2×#67—24no—
410C2×#67—24no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—64no—
418C2×#67—64no—
419C2×#67—64no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67—64no—
423C2×#67—64no—
424C2×#67—64no—
425C2×#67—124no—
426C2×#67—124no—
427C2×#67C22×D314yes—
428C2×#67C22×D314yes—
429C22×Dic3—24no—
430C22×Dic3—24no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—38no—
434C22×Dic3—34no—
435C22×Dic3—34no—
436C22×Dic3—34no—
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—31no—
440C22×Dic3—31no—
441C22×Dic3—34no—
442C22×Dic3—34no—
443C22×Dic3—34no—
444C22×Dic3—61no—
445C22×Dic3—61no—
446C22×Dic3—61no—
447C22×Dic3—64no—
448C22×Dic3—64no—
449C22×Dic3—632no—
450C22×Dic3—64no—
451C22×Dic3—64no—
452C22×Dic3—64no—
453C22×Dic3—64no—
454C22×Dic3—124no—
455C22×Dic3C22×D314yes—
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D311yescharacteristic
458C22×Dic3C22×D311yescharacteristic
459C22×Dic3C22×D311yescharacteristic
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D314yescomplemented
463#237—632no—
464#235—632no—
465C2×D12—34no—
466C2×D12—34no—
467C2×D12—64no—
468C2×D12—64no—
469C2×C4×D3—38no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—34no—
476C2×C4×D3—632no—
477C2×C4×D3—64no—
478C2×C4×D3—64no—
479C2×C4×D3—64no—
480C2×C4×D3—64no—
481C2×C4×D3—64no—
482C2×Dic6—34no—
483C2×Dic6—34no—
484C2×Dic6—64no—
485C2×Dic6—64no—
486C3×C4⋊C4—34no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4—34no—
492C3×C42—34no—
493#217—34no—
494#217—34no—
495#217—34no—
496#217—34no—
497#217—64no—
498#217C22×D314yes—
499#217C22×D314yes—
500#217C22×D314yescomplemented
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—64no—
508(C2×D3)⋊C4C22×D314yes—
509(C2×D3)⋊C4C22×D314yes—
510C4⋊Dic3—34no—
511C4⋊Dic3—34no—
512C4⋊Dic3C22×D314yescomplemented
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—64no—
522C4×Dic3—34no—
523C4×Dic3—34no—
524C4×Dic3C22×D314yescomplemented
525C22×C32—28no—
526C22×C32—22no—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32—22no—
531C22×C32—44no—
532C22×C32C22×D412yes—
533C22×C32C2×#4112yes—
534C22×C32C2×#4112yes—
535C22×C32C2×#4114yescomplemented
536C22×C32C2511yescharacteristic
537C2×C3⋊D3—22no—
538C2×C3⋊D3—22no—
539C2×C3⋊D3—22no—
540C2×C3⋊D3—44no—
541C2×C3×D3—232no—
542C2×C3×D3—28no—
543C2×C3×D3—28no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3C22×D414yes—
549C2×C3×D3C2×#4114yescomplemented
550C32×C4—22no—
551C3⋊Dic3—22no—
552C3⋊Dic3—22no—
553C3⋊Dic3C22×D414yes—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C3×Dic3C22×D414yes—
560C25—31no—
561C2×#41—98no—
562C2×#41—188no—
563C22×Q8—91no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—91no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4D3211yescharacteristic
571C23×C4—31no—
572C23×C4—31no—
573C23×C4—91no—
574C23×C4—91no—
575C23×C4—91no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—98no—
579C23×C4—91no—
580C23×C4—188no—
581#123—98no—
582#123—98no—
583C22⋊Q8—98no—
584C22⋊Q8—98no—
585#121—98no—
586#121—98no—
587#120—38no—
588#120—98no—
589C4×D4—38no—
590C4×D4—98no—
591C4×D4—98no—
592C4×D4—98no—
593#117—98no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C4⋊C4—91no—
599C2×C4⋊C4—91no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—31no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C22⋊C4—91no—
610C2×C42—31no—
611C2×C42—91no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—21no—
625C23×C3—24no—
626C23×C3—34no—
627C23×C3—34no—
628C23×C3—32no—
629C23×C3—32no—
630C23×C3—42no—
631C23×C3—42no—
632C23×C3—42no—
633C23×C3—42no—
634C23×C3—42no—
635C23×C3—68no—
636C23×C3—68no—
637C23×C3—632no—
638C23×C3—62no—
639C23×C3—62no—
640C23×C3—68no—
641C23×C3—62no—
642C23×C3—62no—
643C23×C3#23514yescomplemented
644C23×C3#23714yescomplemented
645C23×C3C23×D312yes—
646C23×C3C23×D312yes—
647C23×C3C23×D312yes—
648C23×C3C23×D312yes—
649C23×C3C23×D311yescharacteristic
650C23×C3C23×D311yescharacteristic
651C22×D3—232no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—28no—
657C22×D3—28no—
658C22×D3—28no—
659C22×D3—32no—
660C22×D3—32no—
661C22×D3—62no—
662C22×D3—62no—
663C22×D3—62no—
664C22×D3—62no—
665C22×D3—62no—
666C22×D3—62no—
667C22×D3—62no—
668C22×D3—122no—
669C22×D3—122no—
670C22×D3—122no—
671C22×D3D3×D414yes—
672C22×D3#23714yescomplemented
673C22×D3C23×D312yes—
674C22×D3C23×D312yes—
675C3×D4—28no—
676C3×D4—28no—
677C3×D4—48no—
678C3×D4—68no—
679C3×D4—68no—
680C2×C3×C4—22no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—34no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—32no—
688C2×C3×C4—32no—
689C2×C3×C4—32no—
690C2×C3×C4—42no—
691C2×C3×C4—68no—
692C2×C3×C4—68no—
693C2×C3×C4—62no—
694C2×C3×C4—62no—
695C2×C3×C4—62no—
696C2×C3×C4—62no—
697C2×C3×C4—62no—
698C2×C3×C4C23×D312yes—
699C2×C3×C4C23×D312yes—
700#67—28no—
701#67—28no—
702#67—68no—
703#67—68no—
704#67—68no—
705#67—68no—
706#67—68no—
707#67—68no—
708#67—128no—
709#67—128no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—28no—
716C2×Dic3—28no—
717C2×Dic3—34no—
718C2×Dic3—34no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—316no—
722C2×Dic3—32no—
723C2×Dic3—32no—
724C2×Dic3—32no—
725C2×Dic3—32no—
726C2×Dic3—64no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—68no—
731C2×Dic3—68no—
732C2×Dic3—68no—
733C2×Dic3—68no—
734C2×Dic3—62no—
735C2×Dic3—62no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—68no—
739C2×Dic3—128no—
740C2×Dic3—122no—
741C2×Dic3—122no—
742C2×Dic3D3×D414yes—
743C2×Dic3C23×D312yes—
744C2×Dic3C23×D312yes—
745C2×Dic3C23×D312yes—
746C2×Dic3C23×D312yes—
747C2×Dic3C23×D312yes—
748C2×Dic3C23×D312yes—
749D12—68no—
750D12—68no—
751C4×D3—316no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—68no—
755C4×D3—68no—
756C4×D3—68no—
757Dic6—68no—
758Dic6—68no—
759C2×C32—24no—
760C2×C32—42no—
761C2×C32#52514yescomplemented
762C2×C32C23×D411yescharacteristic
763C2×C32C22×#4111yescharacteristic
764C2×C32C22×#4111yescharacteristic
765C3⋊D3—42no—
766C3×D3—24no—
767C3×D3—24no—
768C24—31no—
769C24—31no—
770C24—34no—
771C24—64no—
772C24—64no—
773C24—64no—
774C24—91no—
775C24C2×D3211yescharacteristic
776C24C2×D3211yescharacteristic
777#41—1832no—
778C2×Q8—94no—
779C2×Q8—184no—
780C2×D4—24no—
781C2×D4—34no—
782C2×D4—34no—
783C2×D4—64no—
784C2×D4—64no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—94no—
788C2×D4—94no—
789C2×D4—184no—
790C2×D4—184no—
791C2×D4—184no—
792C2×D4—184no—
793C2×D4C2×D3214yes—
794C22×C4—31no—
795C22×C4—34no—
796C22×C4—34no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—64no—
803C22×C4—64no—
804C22×C4—94no—
805C22×C4—94no—
806C22×C4—98no—
807C22×C4—94no—
808C22×C4—94no—
809C22×C4—94no—
810C22×C4—91no—
811C22×C4—94no—
812C22×C4—91no—
813C22×C4—91no—
814C22×C4—184no—
815C22×C4—184no—
816C22×C4—1832no—
817C22×C4—184no—
818C22×C4—184no—
819C22×C4—184no—
820C22×C4C2×D3211yescharacteristic
821C4⋊C4—34no—
822C4⋊C4—94no—
823C4⋊C4—94no—
824C4⋊C4—94no—
825C4⋊C4—94no—
826C4⋊C4—94no—
827C22⋊C4—34no—
828C22⋊C4—34no—
829C22⋊C4—34no—
830C22⋊C4—34no—
831C22⋊C4—34no—
832C22⋊C4—94no—
833C22⋊C4—94no—
834C22⋊C4—94no—
835C22⋊C4—94no—
836C22⋊C4—94no—
837C42—34no—
838C42—94no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—28no—
844C22×C3—28no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—22no—
852C22×C3—22no—
853C22×C3—22no—
854C22×C3—24no—
855C22×C3—21no—
856C22×C3—34no—
857C22×C3—34no—
858C22×C3—42no—
859C22×C3—48no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—42no—
863C22×C3—42no—
864C22×C3—44no—
865C22×C3—44no—
866C22×C3—632no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3—62no—
870C22×C3—62no—
871C22×C3—68no—
872C22×C3—68no—
873C22×C3—84no—
874C22×C3C2×#23512yes—
875C22×C3C2×#23514yescomplemented
876C22×C3C2×D3×D412yes—
877C22×C3C2×D3×D412yes—
878C22×C3C2×#23712yes—
879C22×C3C2×#23712yes—
880C22×C3C2×#23714yescomplemented
881C22×C3D3×#4112yes—
882C22×C3C24×D311yescharacteristic
883C22×C3C24×D311yescharacteristic
884C2×D3—232no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—28no—
890C2×D3—28no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—122no—
898C2×D3—122no—
899C2×D3—122no—
900C2×D3—124no—
901C2×D3—124no—
902C2×D3—244no—
903C2×D3C2×D3×D414yes—
904C2×D3C2×#23714yescomplemented
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—34no—
908C3×C4—42no—
909C3×C4—62no—
910C3×C4—62no—
911C3×C4—62no—
912C3×C4—62no—
913C3×C4—62no—
914Dic3—22no—
915Dic3—22no—
916Dic3—22no—
917Dic3—22no—
918Dic3—22no—
919Dic3—34no—
920Dic3—34no—
921Dic3—64no—
922Dic3—62no—
923Dic3—62no—
924Dic3—62no—
925Dic3—62no—
926Dic3—122no—
927Dic3—122no—
928Dic3C2×D3×D414yes—
929C32C2×#52511yescharacteristic, complemented, Sylow
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—34no—
936C23—34no—
937C23—32no—
938C23—32no—
939C23—68no—
940C23—68no—
941C23—632no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—62no—
946C23—68no—
947C23—92no—
948C23—182no—
949C23—182no—
950C23—182no—
951C23#380414yescomplemented
952C23C22×D3212yes—
953C23C22×D3212yes—
954C23C22×D3211yescharacteristic
955Q8—188no—
956D4—28no—
957D4—68no—
958D4—68no—
959D4—188no—
960D4—188no—
961D4—188no—
962D4—188no—
963C2×C4—22no—
964C2×C4—34no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—68no—
972C2×C4—68no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—916no—
979C2×C4—94no—
980C2×C4—92no—
981C2×C4—92no—
982C2×C4—92no—
983C2×C4—188no—
984C2×C4—188no—
985C2×C4—188no—
986C2×C4—188no—
987C2×C4—188no—
988C2×C4—182no—
989C2×C4—182no—
990C2×C4C22×D3212yes—
991C2×C3—24no—
992C2×C3—24no—
993C2×C3—24no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—44no—
998C2×C3—42no—
999C2×C3—42no—
1000C2×C3—64no—
1001C2×C3—64no—
1002C2×C3—82no—
1003C2×C3#554714yescomplemented
1004C2×C3#558614yescomplemented
1005C2×C3C22×#23511yescharacteristic
1006C2×C3C22×D3×D411yescharacteristic
1007C2×C3C22×D3×D411yescharacteristic
1008C2×C3C22×#23711yescharacteristic
1009C2×C3C22×#23711yescharacteristic
1010C2×C3C2×D3×#4111yescharacteristic
1011D3—24no—
1012D3—24no—
1013D3—122no—
1014D3—122no—
1015D3—242no—
1016C22—28no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—22no—
1022C22—34no—
1023C22—34no—
1024C22—44no—
1025C22—632no—
1026C22—68no—
1027C22—68no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—182no—
1033C22—182no—
1034C22—182no—
1035C22—364no—
1036C22D32×D412yes—
1037C22D3×#23712yes—
1038C22C2×#380412yes—
1039C22C2×#380414yescomplemented
1040C22C23×D3211yescharacteristic
1041C4—22no—
1042C4—34no—
1043C4—62no—
1044C4—62no—
1045C4—62no—
1046C4—62no—
1047C4—62no—
1048C4—94no—
1049C4—182no—
1050C4—182no—
1051C3—21no—
1052C3C2×#554711yescharacteristic, complemented
1053C3C2×#558611yescharacteristic, complemented
1054C2—24no—
1055C2—42no—
1056C2—64no—
1057C2—64no—
1058C2—362no—
1059C2#1059512914yesdirect product factor
1060C2C2×D32×D411yescharacteristic
1061C2C2×D3×#23711yescharacteristic
1062C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C23×D3×Dic3C2semidirect
3. C2×#64148C2semidirect
4. C2×C3×#937C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×#63982C2semidirect
7. C2×#63977C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63971C2semidirect
10. C2×#63969C2semidirect
11. C2×#63952C2semidirect
12. #10595129C2direct (N × H)
13. C2×#63899C2semidirect
14. C2×#63890C2semidirect
15. C2×#63880C2semidirect
16. C2×#63877C2semidirect
22. C22×#638C22semidirect
27. C23×C3×Dic3C22semidirect
28. C22×#627C22semidirect
31. C22×#624C22semidirect
33. C2×#3804C22semidirect
39. C22×D3×Dic3C22semidirect
40. C2×#3757C22semidirect
41. #64148C22semidirect
42. C2×#3752C22semidirect
43. C2×#3750C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#937C22semidirect
48. C3×D4×Dic3C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C2×C3×C4×Dic3C22semidirect
53. #63982C22semidirect
54. #63977C22semidirect
55. Dic3×#67C22semidirect
56. #63971C22semidirect
57. #63969C22semidirect
58. C2×#3724C22semidirect
59. C2×#3724C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
62. C2×#3722C22semidirect
65. C2×Dic32C22semidirect
66. #63952C22semidirect
67. #63899C22semidirect
68. #63890C22semidirect
69. #63880C22semidirect
70. #63877C22semidirect
82. C2×#937D3semidirect
85. C2×D4×Dic3D3semidirect
119. C2×#638C23semidirect
138. C22×C3×Dic3C23semidirect
140. C2×#627C23semidirect
146. C2×#624C23semidirect
152. C2×D3×Dic3D4semidirect
157. #3757C23semidirect
158. #3752C23semidirect
159. #3750C23semidirect
162. C3×#217C23semidirect
165. C3×C4⋊Dic3C23semidirect
166. C3×C4×Dic3C23semidirect
167. #3724C23semidirect
168. #3724C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
171. #3722C23semidirect
174. Dic32C23semidirect
205. C23×Dic3C2×D3semidirect
239. C2×#217C2×D3semidirect
244. #937C2×D3semidirect
247. D4×Dic3C2×D3semidirect
261. C2×C4⋊Dic3C2×D3semidirect
273. C2×C4×Dic3C2×D3semidirect
293. C23×C32#41semidirect
310. C22×C3×D3#41semidirect
348. D3×Dic3C2×D4semidirect
462. C22×Dic3C22×D3semidirect
500. #217C22×D3semidirect
512. C4⋊Dic3C22×D3semidirect
524. C4×Dic3C22×D3semidirect
535. C22×C32C2×#41semidirect
549. C2×C3×D3C2×#41semidirect
643. C23×C3#235semidirect
644. C23×C3#237semidirect
672. C22×D3#237semidirect
761. C2×C32#525semidirect
875. C22×C3C2×#235semidirect
880. C22×C3C2×#237semidirect
904. C2×D3C2×#237semidirect
929. C32C2×#525semidirect
951. C23#3804semidirect
1003. C2×C3#5547semidirect
1004. C2×C3#5586semidirect
1039. C22C2×#3804semidirect
1052. C3C2×#5547semidirect
1053. C3C2×#5586semidirect
1059. C2#10595129direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#38042
C23×D3×Dic32
C2×#641482
C2×C3×#9372
C2×C3×D4×Dic32
C2×#639822
C2×#639772
C2×Dic3×#672
C2×#639712
C2×#639692
C2×#639522
#105951292
C2×#638992
C2×#638902
C2×#638802
C2×#638772
C2×#55863
C2×#55473